June 8 (Reuters) - The Strait of Hormuz will be open but under new conditions to be set by Iran and Oman, including a transit fee, Iran's ambassador to Moscow was quoted as saying on Monday. The U.S.-Israeli war on Iran has largely cut oil flows via the strait, which before the conflict saw one-fifth of the world's oil pass through. Several tankers have managed to leave the Gulf recently, but oil and liquefied natural gas flows are still severely constrained.